(CNN) -- Thousands of firefighters battling to control dangerous wildfires in Arizona will get a small measure of relief this week as winds calm and humidity levels rise, the National Weather Service said Monday.

Critical conditions are forecast Monday across large sections of New Mexico and Texas, and to a lesser extent in Oklahoma and Kansas. On Sunday, critical to extreme conditions could be found in those four states, plus Arizona, Colorado, Utah and Nevada.

The Monument Fire -- which U.S. Forest Service Chief Tom Tidwell has deemed the nation's No. 1 priority, putting it first in line for any air, ground or other resources -- jumped Highway 92 late Sunday afternoon at Carr Canyon heading east, according to the Cochise County website.

"We've had a hard day today, with things that we didn't want to happen," fire spokesman Bill Paxton said Sunday night. "The bull came out of the pen."

Thanks to dry, windy conditions, the fire broke through four contingency lines, including going over to the other side of the highway, said Paxton, part of the national Interagency Incident Management Team.

"Everything aligned for a massive push," he said. "It's really hard on the community here."

The Cochise County Sheriff's Office broadened the evacuation zone east to the San Pedro River, reports InciWeb, an online interagency database that tracks fires, floods and other disasters.

On Sunday evening, the website noted the fire had burned at least 26,956 acres and was 27% contained. More than 1,000 personnel -- as well as 100 engines and nine helicopters -- were battling that blaze, which had destroyed 44 homes and 18 other structures from its start June 12 through Sunday.

The weather has hardly been cooperating in the fight, with humidity at 7% and temperatures topping 96 degrees. The National Weather Service forecast winds should weaken somewhat in the early part of this week, to between 7 mph and 13 mph in Sierra Vista, Arizona, though temperatures were still expected to remain in the 90s or higher all week.

People living in Sierra Vista were ordered to leave Sunday while firefighters conducted burn-out operations in an attempt to stop the fire moving that way, CNN's Thelma Gutierrez reported from the area.

Even as the flames spread, some Sierra Vista residents turned to their faith.

"There are disasters, calamities and tragedies," Tucson Bishop Gerald Kicanas said during a special weekend service at St. Andrew the Apostle Church, reported CNN affiliate KGUN-TV in Tucson.

"We are with them in solidarity," Kicanas said. "We pray for an end to the fire, we pray for the safety of our firefighters and we pray that the monsoon rains will come and free us from these terrible fires that have been so devastating."

The church is taking donations for fire victims.

Will Posko said he is housing several people in his home.

"Our hearts go out to those people," Posko told KGUN. "We all have to help one another in this community."

Parishioner Tom Felix said the community's spirit and support overwhelmed him.

Arizona Gov. Jan Brewer has issued emergency declarations for the Monument Fire and another blaze, Horseshoe II, making Cochise County eligible for $100,000 toward response and recovery expenses.

In Texas, critical fire weather conditions were predicted across much of the state Monday, the Texas Forest Service said.

The forest service is battling 20 wildfires, with 12 new large blazes reported Sunday. Some 500 homes are threatened in Jasper County, the service said, and 163 have been evacuated in Walker County.

Nationwide, wildfires have burned almost as many acres in the first half of 2011 as were recorded by the National Interagency Fire Center for all of last year.

The agency website reports 3.1 million acres in the United States had been ignited by wildfires as of May 31, compared with 3.2 million burned acres cited in the organization's year-end report in November 2010.

One Arizona blaze that started May 29 has mushroomed into a historically large wildfire. Known as the Wallow Fire, it has burned 519,319 acres and was 51% contained as of Sunday evening.

This fire caused power outages Sunday in Arizona cities Blue and parts of Alpine, Nutrioso and Greer, the Navopache Electric Cooperative reported on its website. Generators are powering some of the company's New Mexico customers as well as those in Alpine, Arizona.

Residents of Luna, New Mexico, were ordered to evacuate Saturday afternoon after the blaze jumped containment lines along U.S. 180, according to InciWeb.

But fire public information officer Rich Szlauko had some good news, saying that in terms of bringing the Wallow Fire under control, "Everything is starting to look pretty good."

Some 3,600 people continue to battle the blaze, in the face of winds Sunday measuring 20 mph to 30 mph, he said.

But even with marginally improved conditions, authorities across the Southwest and southern Plains enforced expanded evacuations as flames cut off power to communities.